\(\mathbf {EQ}\)  provides means for determining to what extent the hypothesis automaton produced by the learner approximates the target one. In the case of exact learning, this query checks whether they both produce the same outcome to \(\mathbf {MQ}\)  for all strings.
When \(\mathbf {MQ}\)  are not binary, such as for PDFA, it could be useful to relax equality in order to learn similar hypotheses that tolerate small discrepancies. For instance, in [1]}, [2]}, [3]} equality is replaced by a similarity relation.
However, that similarity relation is not an equivalence as it lacks transitivity.
